How to bisect the segment using a compass ?

How to bisect the segment using a compass ?
You will need:
  • compass
  • line
  • pencil
# 1

The existing problem of how to divide the segment AB at a predetermined ratio, you can start by looking at a simple special case - how to divide the intervalhalf.It can be solved mathematically using vectors, but you can just by using a compass.For this leg of a compass should be diluted to a width greater than half the length of the segment.Setting the compass at point A, it is necessary to hold the first arc.Setting the compass at point B, to hold the second arc.Then it is necessary to note the point of intersection of the two arcs together, C and D. When connecting points C and D get in the intersection of AB and CD segments point O, which would be the midpoint, ie AB = OB.

# 2

To know how to construct a segment equal to this, it is necessary to build on the line and the specified segment AB whose length is known.Then it is necessary to postpone the direct b, at which point it should be noted S. Further, compass measured the length of the

segment AB (one leg of the compass is placed on the point A and the other at point B).On the line b at the point of a compass put one leg and the other leg is marked point D. It turns out the CD segment, the length of which is equal to the present.

# 3

Calculate the value of the function can be given by the formula, with the help of a graph or table.In order to understand how to find the roots belonging to the segment, it is necessary to determine the coordinates of the segment and compared with the roots, given conditions.Thus, the roots of those who will belong to the set of the segment and the segment will be back.

# 4

question of parallel lines is a private matter of threads parallel two lines.To know how to prove that the segments are parallel, it is necessary to designate predetermined lengths, eg AB and CD.You then need to connect with each other, respectively point A to point C, point B c point D. If the length of AC and BD of the resulting segments are equal, it follows that the segments AB and CD - parallel.

# 5

If we know the coordinates of points A and B, which are the ends of the segment AB.Find the coordinates of the point O, which is the midpoint of the segment can be based on the rules that the coordinates of the midpoint (point D) equal to 1/2 of the amount corresponding to the coordinates of the endpoints A and B. How to find the abscissa of the middle of the segment AB: x = (abscissa point A+ abscissa of the point B) / 2 How to find the midpoint ordinate y = (A + ordinate point ordinate of point B) / 2